An example for the above described field of use is the processing of sRGB image data, which are output, for example, by a digital camera and which are processed by an image reproduction system (for example photographic printer or minilab) in such a way that the image which is represented by the image data is produced, for example, by way of a photographic paper.
The sRGB color space and its connection, for example, with the XYZ color space is described, for example, in “The Creation of the sRGB ICC Profile” by Mary Nielson and Michael Stokes, Hewlett-Packard Company, Boise, Id., U.S.A., in Color Research Nr. 568, pages 253-257, 1998. The sRGB color space can be especially popular for the following reasons:                (a) the transfer function and chromaticity of the primary phosphorous colors of cathode ray tubes (CRT monitors) are very similar to the sRGB color space. Thus, images can be shown at reasonable quality on monitors without the need to additionally map the colors by way of a profile. The sRGB color space is by now so common that even in technology fields with transfer functions that strongly deviate from sRGB, for example LCD monitors or plasma monitors, they still support the image data input through an sRGB interface.        b) the manufacturers of digital scanners, monitors and digital cameras often provide as a further feature of their devices that they output RGB image data.        c) almost all computer programs which are conventionally available support sRGB similar color spaces.        
Unfortunately, the sRGB color space and the color space of photographic paper (for example silver halogenide paper) are significantly different (see FIG. 3). Wide regions of the sRGB color space, especially the bright, saturated colors, lie outside the gamut of the photographic paper. Conversely, a monitor normally fails to reproduce the darker, saturated colors of the photographic paper.
In order to adapt the range of the colors (input gamut) which can be captured by the input device to the range of the colors (output gamut) which can be reproduced by the image reproduction system, the following two processes are currently used:                (1) The sRGB data are simply used as image control data to control the image reproduction system. In other words, the sRGB coordinates are interpreted and used as RGB coordinates for the control of a printer by way of its RGB input. This process is extremely simple and guarantees that all printable colors of the printer can be exploited (when the range of values of the sRGB coordinates matches the range of values of the RGB coordinates).        (2) The classical color management approach is used. With respect to color management, reference is made to “Appendix A: Colorimetry” in “Digital Color Management” of E. J. Giorgianni & T. E. Maddon, Addison-Wesley, Massachusetts, 1997, pp. 440-445, (ISBN 0-201-63426-0). The principle of a device independent platform which represents a central point of the color management, is also described in the article “Color Management: Current Practice and the Adoption of a New Standard” by Michael Has and Todd Newman which is available at the internet address http://www.color.org/wpaper1.html. According to the classical color management approach, the input sRGB coordinates are transformed into color coordinates of a color space platform (in the following abbreviated as PCS for “profile connection space”). The color space platform is preferably a device independent color space. Thus, the gamut of the color space platform preferably encompasses all possible or actually present gamuts of the input devices and output devices. An image with a given gamut in the color space platform (PCS) is mapped onto the nominal color space and then converted into RGB device coordinates of the output device (image reproduction device).        
Besides the above mentioned processes, the following process are also possible:                (3) One starts with a preselected color pallet or test scenery. One captures the color pallet or test scenery both by way of a conventional photographic apparatus with film as well as with a digital image capturing system (for example digital camera or scanner). The data are then processed, whereby analog techniques are used in the conventional photography and digital processes are used in the digital image capturing. The two results are compared and a profile is produced in order to change the digitally captured data until a printout based on the digital data corresponds to the printout of the analog system (conventional photography).        
However, each of the above mentioned processes has its weakness:                (1) Process 1 violates the principles of the color management. It is one of the essential principles of color management to achieve a color perception which comes as close as possible to the color perception of the original image. However, strong shifts and distortions occur between the sRGB color space and the printer color space. They are mutually rotated and twisted. However, the process 1 simply maps corners onto corners of the respective color space. The hue, saturation and brightness are thereby not at all maintained during the mapping. This leads to a color reproduction which has very little in common with the color impression of the original image. It is a direct cause of this solution, as the inventors have recognized, that the color properties of the photographic paper are recognizable. For example, the greenish yellow of a lemon, which corresponds to the yellow corner of the sRGB color space, becomes orange on the photographic paper. In similar manner, the bright monitor green is reproduced as a dark green on the photographic paper. In summary, this process has little in common with standard color management principles. The user is left alone with the actual color management. He must manually preprocess the data before the input into the printer in order to achieve the desired colors.        
The sRGB color space includes many highly saturated, very bright colors, which cannot be reproduced with a photographic paper. The inventors have recognized that standard color management programs according to the above process number 2 must find a compromise between the preservation of the hue, the saturation and the brightness. These bright, strongly saturated colors are thereby mapped onto very bright pastel colors. Although this is mathematically correct, this is often not the color which an observer would expect. This applies especially for graphics or colored text. When large regions of the sRGB color space are outside the portion of the color space reproducible by the paper, which means outside the color gamut of the photographic paper, wide regions of the sRGB gamut are compressed onto a small region when after the mapping of the sRGB gamut into the color space platform (PCS) the unavoidable gamut compression takes place upon the gamut mapping into the color space of the output device (image reproduction system or printer). This compression of significant portions of the sRGB gamut leads to a loss in contours, especially for bright, highly saturated colors. On the other hand, the sRGB gamut, which means the color space stretchable by the sRGB data, covers only a portion of the photographic paper gamut, which means the colors reproducible by the photographic paper, namely in the range of the dark colors. These dark colors do not occur in the sRGB color space of the input device and are therefore never used for a printout in the process according to point number 2. In other words, a significant portion of the available photographic paper gamut or printer gamut is not used.
The inventors have, for example, discovered that the third process provides better color reproduction results than the processes 1 and 2, namely in the case of the reproduction of digital image data (which, for example, are stored on a digital medium) on a photographic paper. The process 3 can however, be hard to generalize and can be inflexible. The process 3 requires the use of a concrete photographic paper and a concrete color chart. It is thereby assumed that the specifically used photographic paper is a generally valid reference paper and that the colors reproduced on the color chart cover all possible colors. However, at least each concrete photographic paper has its advantages and disadvantages and, thus, is not optimal. Since the process is based on measurements, the color transformation cannot be parameterized and thereby adapted to other cases, especially to other photographic papers. The reason for that is especially that the color transformation has black box properties.